Earlier this month Wilson, 67, was sentenced to a year in detention after becoming one of the highest-ranking church officials to be convicted on the charge.
“The Holy Father Francis accepted the resignation of the pastoral government of the Archdiocese of Adelaide (Australia), presented by S.E. Mons. Philip Edward Wilson,” the Vatican said in a statement.
His resignation comes less than a fortnight after Australian Prime Minister Malcolm Turnbull asked the pope to sack Wilson, who was found guilty in an Australian court of failing to report allegations against paedophile priest Jim Fletcher.
He had long denied the charges and initially resisted calls to resign pending an appeal against his conviction.
Wilson’s legal team made four attempts to have the case thrown out, arguing that he suffered from Alzheimer’s and so should avoid trial.
But a magistrate in Australia found Wilson guilty of concealing a serious indictable offence of another person, concluding that his primary motive was to protect the church.
He said when sentencing him that Wilson showed “no remorse or contrition”.
The court has adjourned the matter until August 14 to assess whether Wilson can serve his sentence under home detention.